Hyperbolic sine-correlated beams

Statistical properties of circular and rectangular multi-sinc Schell-model beams propagating in uniaxial crystals

With the extended Huygens-Fresnel principle, we derive the expressions for the spectral intensity, coherence, and effective beam width of circular and rectangular multi-sinc Schell-model (MSSM) beams propagating through uniaxial crystals. Numerical simulations are employed to extensively explore how beam and crystal parameters modulate the optical field. The results reveal that the propagating field exhibits multiple ring-shaped and array-like intensity distributions, with adjustable features such as the number of concentric rings, central brightness, array dimensions, and the morphology and diversity of sub-beams. Additionally, the spectral coherence displays an oscillatory distribution that evolves into a Gaussian distribution as the transmission distance increases. The anisotropy of uniaxial crystals not only influences the morphology of intensity distribution but also affects the evolution rate of coherence and the expansion rate of effective beam width. Our work contributes to optimizing beam propagation through uniaxial crystals, potentially benefiting precision optical systems in laser technology.

Partially coherent Pearcey-Gauss source with hyperbolic sine correlation of the spatial spectrum

By designing the intricate coherence structure, we are able to create a desired beam profile and trajectory. Our research focus lies on the Fourier plane, specifically emphasizing the coherence of spatial frequencies, and we find it can be seen as a constant system response. A theoretical framework is developed, and experimental studies are conducted to generate a light field of the spatial spectrum with a complex correlation using the pseudo-mode superposition method. We successfully produce partially coherent Pearcey-Gauss beams whose spatial spectrum is hyperbolic sine correlational. Interestingly, these beams maintain the distinctive propagation properties of the Pearcey pattern while exhibiting the remarkable ability to split the mainlobe into two separate lobes.

Enhancing fiber-coupling efficiency of beam-to-fiber links in turbulence by spatial non-uniform coherence engineering

We present a general formula for the fiber-coupling efficiency of various types of non-uniformly correlated beams propagating in a turbulent atmosphere. With it, we calculate the fiber-coupling efficiency of a specific type of non-uniformly correlated beams, Laguerre non-uniformly correlated (LNUC) beams, to investigate how the non-uniform correlation structure plays a role in enhancing the fiber-coupling efficiency. Compared with conventional Gaussian Schell-model beams, the LNUC beams possess better coupling behavior, and the initial coherence length and beam order of such beams can be adjusted to further improve the fiber-coupling efficiency in turbulence. Our results demonstrate how non-uniformly correlated beams can be used for fiber-coupling applications, and demonstrate their intriguing potential for free-space optical communications.

Asymmetrical inseparable coherent structures

A novel, to the best of our knowledge, class of coherent structures of inseparability, incorporating phases asymmetrically cross-coupled by two position vectors, is introduced in theory and experiment. These phases disappear in the environment of complete coherence, but the vanishment is avoidable in the coexistent state of extreme incoherence and full coherence. The radiated beams intrinsically possess a controllable rotation but undergo an intermediate process quite different from the twisted Gaussian Schell-model beams. Analysis shows a novel association between the magnitude and the phase of the coherent structure which displays both synergy and opposition. Our work further reveals the inner mechanism of the inseparable coherent structures and extends a new horizon for the optical twist.

Special correlation model sources producing a self-focusing field

We evaluate the modes for non-Schell-model sources whose degrees of spectral coherence depend on the difference of the special function values of the position coordinated of two points. It is shown that such sources modulated by various function possess different spatial coherence properties, and cause them to produce the self-focusing fields with different characteristics. The results suggest a convenient method for modeling novel classes of partially coherent self-focusing optical fields.

Multi-hyperbolic sine-correlated beams and their statistical properties in turbulent atmosphere

We introduce a partially coherent beam, called a multi-hyperbolic sine-correlated (MHSC) beam, by employing a multi-hyperbolic sine function to modulate the spectral degree of coherence. Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function, we derive the analytical expressions for the spectral intensity, the root-mean-square (rms) angular width and the M² factor in turbulent atmosphere. Numerical results show that the intensity profile, which keeps the dark-hollow invariant in free space, will be gradually destroyed by the turbulence along the propagation distance. We believe that the MHSC beams have significant advantage over the hyperbolic sine-correlated beams for reducing the turbulence-induced degradation, especially for the MHSC beams with a higher beam order N. The effects of the beams parameters and the turbulent atmosphere on the beam quality are analyzed in detail.

Random source for generating Airy-like spectral density in the far field

A stationary beam forming an Airy-like spectral density in the far field is analyzed theoretically and experimentally. The Schell-model source that radiates such a beam is an extended version of a recently introduced source [O. Korotkova, et al., Opt. Lett.43, 4727 (2018)10.1364/OL.43.004727; X. Chen, et al., Opt. Lett.44, 2470 (2019)10.1364/OL.44.002470, in 1D and 2D, respectively]. We show, in particular, that the source degree of coherence, being the fourth-order root of a Lorentz-Gaussian function and having linear and cubic phase terms, may be either obtained from the Fourier transform of the far-field Airy-like pattern or at the source using the sliding function method. The spectral density of the beam is analyzed on propagation through paraxial ABCD optical systems, on the basis of the generalized Collins integral, by means of the derived closed-form expression. We show that the distribution of the side lobes in the Airy beam spectral density can be controlled by the parameters of the source degree of coherence. Further, an experiment involving a spatial light modulator (SLM) is carried out for generation of such a beam. We experimentally measure the complex degree of coherence of the source and observe the gradual formation of a high-quality Airy-like spectral density towards the far field. In addition, the trajectory of the intensity maxima of the beam after a thin lens is studied both theoretically and experimentally. The random counterpart of the classic, deterministic Airy beam may find applications in directed energy, imaging, beam shaping, and optical trapping.

Spatial superbunching of light. Model sources

Sources that exhibit superbunching in the spatial domain are discussed. A few model sources are presented with the pertaining probabilistic treatment. Schemes for the experimental realization of similar sources are suggested, and the results of simulated tests are given.